The ratio of volume of $\mathrm{Al}^{27}$ nucleus to its surface area is (Given, $R_0=1.2 \times 10^{-15} \mathrm{~m}$)

Consider the nuclear fission reaction ${ }_0^1 n+{ }_{92}^{235} \mathrm{U} \longrightarrow{ }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+3{ }_0^1 n$. Assuming all the kinetic energy is carried away by the fast neutrons only and total binding energies of ${ }_{92}^{235} \mathrm{U},{ }_{56}^{144} \mathrm{Ba}$ and ${ }_{36}^{89} \mathrm{Kr}$ to be $1800 \mathrm{MeV}, 1200$ MeV and 780 MeV respectively, the average kinetic energy carried by each fast neutron is (in MeV)

The natural logarithm of the activity $R$ of a radioactive sample varies with time $t$ as shown. At $t=0$, there are $N_0$ undecayed nuclei. Then, $N_0$ is equal to [Take $e^2=7.5$ ]

In the Rutherford's alpha scattering experiment, as the impact parameter increases, the scattering angle of the alpha particle